Hi ngh ton quc v iu khin v T ng ho - VCCA-2011 VCCA-2011 Thit k
b iu khin cun chiucho mch vng in p mt chiu ca nghch lu ngun Z
Design method of backstepping control for closed loop DC voltage
ofZ source inverter Trn Trng Minh, V Hong Phng Trng HBK H Ni
e-Mail: [email protected],
[email protected] Tm tt Bibonytrnhbyphngphpthitkbiu
khincunchiuchomchvnginpmtchiu da trn m hnh tn hiu trung bnh camch
tng ng pha mt chiu nghch lu ngun Z (ZSI). Lut iu khin arac kimnghim
bngm phng viphnmmMatlab/Simulink/Plecsvimchin
tngngphamtchiucaZSI,chngtin p trn t c n nh theo gi tr mong mun
trong c 2 trng hp in p DC bin thin vkhng bit tham s ti
Abstract:Thispaperpresentsadesignmethodofbackstepping control for
closed loop DC voltage on averaged model
ofZ-sourceinverterequivalenceDCcircuit.The
presentedcontrolrulesforequivalenceDCcircuitof
ZSIisverifiedbysimulationusingMatlab
/Simulink/Plecssoftwware,thatprovescapacitor voltage maintains
desired value in two cases: variable DC voltage and unknown
parameter load. K hiu K hiun v ngha EVinpDCcungcpcho nghch lu ngun
Z uC, UCVinptrungbnh,xclp trn tiL, ILADngintrungbnh,xc lp qua cun
cm d, DTsshootthroughtrung bnh, xc lp Ch vit tt ZSIZ source
inverter VSIVoltage source inverter EMIElectronmagnetic
interference MSVMModify space vector modulation 1.Phn m u Nghch lu
ngun Z (ZSI, s cho trn hnh H.1) c phnmtchiubaogmphntLCxptheohnh ch
X, mch van l nghch lu ngun p (VSI) truyn
thng,angcnhiungiquantmnghincu araccngdngthct.CutrcZSIkhc phc c mt s
nhc im ca VSI truyn thng: in p u ra khng cn b gii hn bi in p mt
chiunhVSI;mchiuchkhngcnbtc ngbithigiancht(deadtime)lnguynnhn gy
nhiu in t (EMI) trong h thng. Hn na, ZSI
lmviclinhhottrongc2chbtnggimp (boost bucks) thng qua vic iu khin t
s shoot through d v t s bin iu ma ph hp [1]. V
vy,ZSIcxemnhmtphngnkhthichophp iu khin in p u ra t gi tr mong mun
trong khiinpuvobinng.Vinhngcim ,ZSImratrinvngngdngchoccngun nng lng
phn tn nh pin nng lng mt tri, fuel cell,scgiminpurabinngnhiu theo
cc iu kin mi trng lm vic khc nhau.L1L2C1 C2EAC
loadDCcontrollerMSVMdG1G4 G6 G2G5 G3DUcuC, iL*ma H. 1Cu trc iu
khinnghch lu ngun Z. Mchiuchvectorkhnggian(MSVM)choZSI vi u vo l t
s bin iu ma yu cu, khng khc nhiulmsovinghchluVSIthngthng.Tuy nhin
phn mch mt chiu s yu cu c mch vng iu chnh in p vi lng t l gi tr in
p trn tmongmun,uracabiuchnhlts shootthroughdasangmchiuchMSVM.
Nhiutcngcthlsthayicangunmt chiu E, s bin ng ca ph ti tng ng t pha
mchxoaychiu.Mchvnginpmtchiuc thdng b iu chnh PIDtuyntnh, c thitk
trnmhnhtnhiunhtheophngphptuyn tnhhaquanhimlmviccnbng[2],[3],[4]. iu
ny c th gp kh khn khi thit k tham s b iu chnh vi i tng lm vic ti
nhiu im cn bng khc nhau. Trongbibonychngtimunthnghim
phngphpthitkcunchiu(backstepping)cho mchvnginpmtchiucaZSIdatrnm
hnhtnhiutrungbnhmangcimphituyn.Phngphpcunchiucngdngchob bin i DC DC
kiu boost vi nh gi c th cho 2 gii php iu khin in p ra trc tip v gin
tip thngquadngquacuncm[5].yccbc 696Hi ngh ton quc v iu khin v T ng
ho - VCCA-2011 VCCA-2011 thit k tin hnh tng t nh trong [5], vi c s
l thuyttrong[6],nhngviskhcbitvicphn tch c im ng hc khng (zero
dynamic) ca i tngtrc,tarathuttoniukhincun
chiugintipiukhininptrntthngqua dng in qua cun cm. 2.M hnh ton hc
phn DC ca ZSI Theo[1]coicckhabndnnghchluvphti xoay chiu c i din bi
dng it v kha bn dn S ta cmhnhmchtngngnhn t phamt chiu ca nghch lu
ngun Z. L1L2C1 C2EDSit H. 2Mch tng ng ZSInhn t pha mt chiu.
TmhnhmchtngngtrnhnhH.2,trong mi chu k iu ch c hai ch lm vic tng ng
trngthingctkhabndnS,diodeD:shoot
through(S:on,D:off);non-shootthrough(S:off,
D:on).MiquanhgiainptrntC(uC),in p nh ( i u ) t ln nhnh van ZSI vi
in p ngun (E) tun theo quan h (1). 1,1 2 1 2iCd Eu E ud d(1) Trong
(1) t s shoot through d (0 d < 0,5) l thi gian ng in tng i ca
kha S. iu khin t s d th s iu khin c kh nng tng p ca ZSI so vi in p
ngun vo E.MhnhtonhcmchvnginpmtchiuZSI cxydngtheophngphpkhnggiantrng
thi trung bnh [2] vi cc gi thit: -Mng Z i xng: L1 = L2, C1 = C2. V
vy, uC1 = uC2 = uC, iL1 = iL2 = iL. -Cc kha bn dn D, S l l tng. -Ch
dng in lin tc. M hnh tn hiu trung bnh phn DC canghch lu ngun Z vi
in tr ti tng ng R biu din h phng trnh (2). (2 1) (1 )(2 )(1 2 ) (
1)LCC CLdiL d u d Edtdu u EC d i ddt R(2)
tbintrngthixT=[x1x2]T=[iLuC]T vitli(2) nh h phng trnh trng thi (3).
122 21(2 1) (1 )(2 )(1 2 ) ( 1)dxL d x d Edtdx x EC d x ddt R(3) T
(3) gi tr xc lp ca in p trung bnh trn t v dng in trung bnh qua cun
cm biu din nh (4). 2 1(2 ) 1 1;2 1C CC LU U E DX U E X ID R E(4)
Sauycnkhosttnhnghckhng(zero dynamic) ca h (3) i vi bin trng thi x1,
x2. -nghcvibintrngthix2.Thphng trnh(3)trittiubinx1vviphpbini
tonhcrtraphngtrnhviphnivitn hiuiukhindnh(5),xttiimcnbng *2 2x x .
2*2*2(2 1)(2 1) (1 )( 2 )R dd x d d EL E x(5) Cho0 d phng trnh (5)
c im cn bng kp d1,2 v d3 nh (6). 1,2*23*20, 52dx Edx E(6)
0.5dd03dVng lm vict s shoot through H. 3Phn b im cn bng phng trnh
(5). Biudinphngtrnh(5)vccimcnbng(6) trn th nh hnhH.3 cho thykhng tn
ti im cn bng n nhtrongvnglmvic(0 0 c la chn khi thit k.
Vxcnhmtatbiuthctrongngocvung(21) bng 0 1 2 2 22 1 0 + + = ( d )z c
z z(22) Thay (18) vo (22) rt ra lut iu khin t s shoot through nh
(23). 2 2 2 1 21 2 2 1 1 1 2122 1 2 1 2 1 1 2 1 2 12 ( + + + `
)=refx ( x E )( d ) z c z ( d ) ( d ) ( d )( d ) c z ( d )c z ILC
RLCdE( )Lo(23)DC-DCZ source inverterPhng trnh
(23)TnhIrefEUrefiLuCIrefPWMd00,5Gii hn H. 5Cu trc iu khin cun chiu
cho mch vng in p mt chiuca ZSI. 698Hi ngh ton quc v iu khin v T ng
ho - VCCA-2011 VCCA-2011 T phng trnh (23) ch racu trciukhin cun
chiu cho mch vng in p mt chiu ZSI vi ti R xc nh nhH.5.
-Khosttnhnnhcacutrciukhin cun chiu vi tham s ti R xc nh.Thay lut iu
khin (23) vo (18)tac m hnh i tngmchvnginpmtchiu(3)cmt li trn khng
gian trng thi mi (z1, z2) nh(24). 1 2 1 12 1 2 22 11 2= = z ( d )z
c zz ( d )z c z(24) H (24) c im cn bng (z1, z2) = (0,0). Xt hm V xc
nh dng nh (25). 2 21 21 12 2V z z = +(25) Ly o hm (25) thu c o
hmVnh (26).1 1 2 2= + V z z z z(26) Thay (24) vo (26) ta c o hmVnh
(27). 2 21 1 2 2= V c z c z (27) Vi c1, c2 > 0 hmVxc nh m.T , h
(24) n nhtimcntiimcnbng(z1,z2)=(0,0).Do
,x1tintinnhtheoIrefvtheo(4)x2tinti n nh theo Uref. 3.2 iu khin cun
chiu vi tham s ti bt nh TrongtrnghpphtiphaxoaychiucaZSIbin i, vic
xc nh tham s R a vo lut iu khin (23) gp nhiu kh khn. V vy, gii php
a ra trong trng hp ny s dng thut ton iu khin
cunchiuthchnghi.Trnhtthitkthutton iu khin cun chiu thch c thc hin
ging nh trongmc3.1, tuynhinhm Vc b xung thm phn sai lch c lng tham
s ti t = 1/R h phng trnh (3) tr thnh h c tham s bt nh (uncertainty
equivalence). 1221 2(2 1) (1 )(1 2 ) ( 1)(2 )dxL d x d EdtdxC d x d
x Edtq(28) T(28)gitrxclpcainptrungbnhtrnt v dng in trung bnh qua
cun cm nh (29). 2 1(2 ) 1;2 1C CC LU U E DX U E X ID Eq (29)
Vgitrdngclng: (2 )C CLU U EIEq vi q gi tr c lng tham s ti.
Bc1:tsailchgiabintrngthix1vdng in t c lngef r Il z1:1 1= ref z x I
Ly o hm z1 nh (30). 21 12 1 1 = = + ref refx E z x I ( d ) ( d ) IL
L(30) Trong(30)x2/Llbiniukhino,t(30)rtra biu thc xc nh x2/L nh
(31). 1212 1 ( + ( =refEz ( d ) Ix LL d(31) t 1 1 1= z c z , trong
hng s c1 > 0 c la chn khi thit k. Vit li phng trnh (31) nh (32).
1 1212 1 ( + ( =refEc z ( d ) Ix LL d(32) Tuy nhin thct th x2 l bin
trng thi, do hm tm c (32) ch l hm mong mun x2/L v c t 1 xc nh nh
(33). 1 1112 1 ( + ( =refEc z ( d ) ILdo(33) 1 c gi l hm n nh
(stabilization function). t sai lch x2/L v 1 l z2: 22 1xzLa(34)
Thay (32), (33), (34) vo (30):1 2 1 12 1 z ( d )z c z = (35) Bc 2:
Ly o hm (34), c o hm z2 nh (36). 22 1xzLo = (36) Trong :1 221 21 2x
( d )( x E )x ( d )C Cu = +(37) Vi u u u = + (u sailchclngthamsti)
phng trnh (37) vit li nh (38). 1 221 21 2x ( d )( x E )x ( d ) ( )C
Cu u = + + (38) Ly o hm (33), c o hm 1 nh (39). 21 1 1 21 12 122 1
2 1 ( + ( = + refc z ( d )c z Id E( )d L do o (39) Th vo (38), (39)
vo (36) c o hm 2znh (40). 1 222121 1 1 21 21 21 222 12 12 1 = + + (
+ ( refx ( d )( x E )z ( d )LC LC( d )( x E ) d E( )LC d Lc z ( d
)c z Iduu o (40) Xt hm V xc nh dng nh (41). 2 2 21 21 1 12 2 2= + +
V z z u(41) Vi>0gilhsthchnghivclachn trong qu trnh thit k. Ly o
hm(41).1 1 2 21= + + V z z z z uu(42) Th (35), (40) vo (42) qua vi
php bin i ton hc ta c: | | | |2 21 1 2 2 2 1 2V c z c z z A A u = +
+(43) Trong hng s c1 > 0 c la chn khi thit k. V
xcnhmthtatccbiuthcA1,A2 bng 0:A1 = 0, A2 = 0 (44) 699Hi ngh ton quc
v iu khin v T ng ho - VCCA-2011 VCCA-2011 Vi A1 = 0 rt ra hm iu
khin t s shoot through nh (45). 2 2 2 1 21 2 2 1 1 1 2122 1 2 1 2 1
1 2 1 2 12 ( + + + ` ( )=refx ( x E ) ( d ) z c z ( d ) ( d ) ( d
)( d ) c z ( d )c z ILC LCdE( )Luo(45)DC-DCZ source inverter Phng
trnh (45)TnhEUrefiLuCuuCz2EPhng trnh (46)PWMd00,5Gii hn ef r Ief r
IH. 6Cu trc iu khin cun chiu thch nghicho mch vng in p mt chiuca
ZSI. Vi u u = lutthch nghi thams khiA2=0 c xc nh nh (46). 221 2 ( d
)( x E )zLCu =(46) T phngtrnh (45), (46) ch racu trciukhin
cunchiuthchnghichomchvnginpmt chiu ZSI vi ti R khng xc nh nhH.6.
-Khosttnhnnhcacutrciukhin cun chiu thch nghiThay lut iu khin (45)
vo (40)tac m hnh i tngmchvng in pmt chiu(28) c m t
litrnkhnggiantrngthimi(z1,z2,u )nh (47). 1 2 1 122 1 2 2222 11 21
21 2 = = + = z ( d )z c z( d )( x E )z ( d )z c zLC( d )( x E
)zLCuu (47) H c im cn bng (z1, z2, u ) = (0,0, 0). Xt hm V xc nh
dng nh (48). 2 2 21 21 1 12 2 2= + + V z z u(48) Ly o hm (48) thu c
o hmVnh (49).1 1 2 21= = + + V V z z z z uu(49) Thay (47) vo (49)
ta c o hmVnh (50). 2 21 1 2 2= V c z c z (50) Vi c1, c2 > 0
hmVxc nh m.T , h (47) n nh tim cn ti im cn bng (z1, z2,u ) = (0,0,
0). Do , x1 tin ti n nh theoref I ,uhi t theo , dn n x2 tin ti n nh
theo Uref. 4.Kt qa m phng Thut ton iu khin cun chiu cho mch vng in
pmtchiucaZSIcmphngkimchng bngphnmmMatlab/Simulinks/Plecsvithams m
phng. DC voltage E150V Tn s pht xung PWM10 kHz C1 = C2 = C235 uF L1
= L2 = L0,6 mH H s c1 = 1000, c2 = 5000, = 10-11 Trng hp 1:in p
ngun DC vo bin thin vi tham s ti R = 10 . in p t Uref = 250 V, in
pE=150Vtrongkhongt0,3s,E= 130V trong khong 0,2s < t < 0,3s.
Kt qu m phng th hin t hnh H.7 H.10. Nhn xt: Vi in p E bin thin in p
trn t C (uC) c gi bng gi tr t, cn in p nh( i u )
tlnnhnhvantnglndosthayicats shootthrough.Tuynhin,gitrtrungbnhca in
p t ln nhnh van vn c gi bng uC. Trnghp2:Thutiukhincunchiuthch nghi
khi tham s ti Rt = 10 (t = 0,15s 0,3s) v Rt =20(t0,3s). in p
tUref=250 V, E = 150V. Kt qu m phng th hin t hnh H.11 H.15.
Nhnxt:Khithamstibinthinvkhngbit trc, gi tr c lng hi t bng gi tr thc
sau 1khongthigian.Vvy,tsshootthrough ciukhingitheogitrxclpmongmun
nn in p trn t bng hng s theo gi tr t.700Hi ngh ton quc v iu khin v
T ng ho - VCCA-2011 VCCA-2011 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0.45 0.5050100150200250300UcE H. 7in p trn t C vi in p E thay i. 0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.5050100150200250300350400450 H. 8in p t ln nhnh van vi in p E
thay i. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.500.050.10.150.20.250.30.350.40.450.5 H. 9T s shoot through d vi
in p E thay i. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.5020406080100120 H. 10Dng in qua cun cm vi in p E thay i. 0 0.1
0.2 0.3 0.4 0.5050100150200250300 H. 11in p trn t C vi tham s ti
thay i. 0 0.1 0.2 0.3 0.4 0.5050100150200250300350400450 H. 12in p
t ln nhnh van vi tham s ti thay i. 0 0.1 0.2 0.3 0.4
0.5-0.0200.020.040.060.080.1 H. 13Tham s ti c lngqvi tham s ti thay
i. 0 0.1 0.2 0.3 0.4 0.500.050.10.150.20.250.30.35 H. 14T s shoot
through d vi tham s ti thay i. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0.4 0.45 0.5010203040506070 H. 15Dng in qua cun cm vi tham s ti
thay i. 5.Kt lun Bi bo trnh by thit k b iu khin cun chiu
chomchvnginpmtchiucaZSI,kim chng bng m phng cho thyin p trn t C gi
bng gi trt trong c hai trng hp ti khng xc nhvkhingunpcpuvobinng.Tuy
nhin, thut ton cun chiuc mt s c im: i
hithngtinchnhxcvthamsL,C,nhhng bi tn s pht xung nn m bo trit tiu
sai lch tnhcthbxungthmthnhphntchphnvo lut iu khin, xut hin cc thnh
phn o hm bc cao trong lut iu khin. V vy, cc nghin cu tip theo cn nh
gi thm b iu khin ny vi m hnh thc nghim ZSI trong phng th nghim. Ti
liu tham kho
[1]FangZhengPeng:Z-sourceinverter.IEEEtransactionsonindustryapplications,vol.39,
no.2, March/April, 2003.[2]JingboLiu,JiangangHu,andLongyaXu;
DynamicModelingandAnalysisofSourceZ Converter-Derivation of AC
Small Signal Model andDesign-OrientedAnalysis;IEEE
transactionsonindustryapplications,vol.22, no. 5, Seember 2007.
[3]XinpingDing,ZhaomingQian,ShuitaoYang,
BinCuil,FangzhengPeng:APIDControl
StrategyforDC-linkBoostVoltageinZ-source
Inverter.AppliedPowerElectronics Conference,APEC2007-TwentySecond
Annual IEEE. [4]GokhanSen,MalikE.Elbuluk:Voltageand
Current-ProgrammedModesinControlofthe
Z-SourceConverter.IEEEtransactionson industry applications, vol.
46, no. 2, march/april 2010. [5]H.ELFALIL,F.GRIRI:BacksteppingBased
ControlofPWMDC-DCBoostPower Converters.IEEEInternationalSymposiumon
Issue Date: 4-7 June 2007, ISIE 2007.
[6]Krstc,M.;KanellakopoulosI.;Kokotovc,P.:
NonlinearandAdaptiveControlDesign.John Wiley & Sons, Inc., New
York 1995. [7]RomeoOrtega,AntonioLora,PerJ.
Nicklasson,HeberttSira-Ramrez:Passivity
basedControlofEulerLagrangeSystems:
Mechanical,ElectricalandElectromechanical Applications. Springer,
May 1998. 701Hi ngh ton quc v iu khin v T ng ho - VCCA-2011
VCCA-2011 Ph lc c c s nh gi hiu qu ca b iu khin thit
ktrongbibony,tcgitinhnhsosnhm phngvicutrciukhinkhintuyntnhPID
[3],[4]cthitktrnmhnhtnhiunhvi im lm vic cn bng cn c xc nh trc. Cu
trc b iu khin tuyn tnh PID nh (51) 0(1 )(1 )( ) (51)(1 )Lzc cpssG s
Gseee+ +=+
Trong : 1 sin 1 sin1 sin 1 sinz c p cf f f fu uu u += =+ 01| |(
). ( )Cc f fdt CGG s G s== fc chn bng 1/10 tn s ct xung (fc =1kHz).
d tr pha b b ti tn s fc ( = 410) Tham s m phng c xt nh trng hp 1 mc
4, kt qu m phng c ch ra trong hnh t H.16 H.19. H. 16in p trn t C vi
in p E thay i. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.5-200-1000100200300400500 H. 17in p t ln nhnh van vi in p E thay
i. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.500.050.10.150.20.250.30.35 H. 18T s shoot through d vi in p E
thay i. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.501020304050607080 H. 19Dng in qua cun cm vi in p E thay i.
Ktqumphngchngtbiukhinchomch vnginpmtchiuZSIcthitktheo phng php cun
chiu t ra c hiu qu khi so snh vicutrciukhintuyntnh,inptrntC
nhanhchngtgitrnnh,khngcpmch trong tn hiu iu khin t s shoot through
y l tn hiu quan trngquytnhnchtlngin p, dng in trong iu khin ZSI.
Tuynhin,biukhincthitktheophng php cun chiu i hi thng tin chnh xc
tham s, thng tin o lng tn hiu trung bnh in p trn t,
vdngquacuncm,iunycthsgpkh khn khi trin khai cu trc ny trong thc t.
V vy, cn c nghin cu su hn v cu trc iu khin ny s dng trong ZSI vi cc
ng dng khc nhau trong thc t. Tiu sTrnTrngMinhsinh nm1960, ti
VitNam. T nm19781983hctiihcBchkhoaBacu
(LinXc).NhnbngM.StiAIT-ThiLannm 1997,bngTinschuynngnhTngha
XNCNtrngihcBchKhoaHNi (HBKHN) nm 2008. T nm 1984, cng tc ti b
mnTnghaXNCNkhoainHBKHN. Lnh vc nghin cu: iu khin in t cng sut, b
binicngsutln,bintnmatrn,ngdng in t cng sut trong li in thng minh, b
bin i DC-DC hiu sut cao, lc tch cc, V Hong Phng sinh nm 1983, ti
Vit Nam. Nhn bng k s nm 2006,Thcsnm2008chuyn ngnhTnghaXNCNkhoa
in-HBKHN.Hinangl Nghincusinhkha20102014 chuynngnhThitbvhthng iu
khin t ng - HBKHN. T nm 2006 n nay cng tc ti Trung tm Nghin cu
cngnghcaoHBKHN.Lnhvcnghincu: iukhinintcngsut,ngdngintcng sut trong
li in thng minh,.. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
0.5050100150200250300702
